Vacancy Loops Research Articles

Effect of gaseous impurity atoms on the formation of microvoids studied by positron annihilation

Positron annihilation techniques have been applied to study the nucleation, growth and annealing of voids and gas bubbles. This technique is extremely powerful for the study of microvoids and microbubbles which are too small to be observed by electron microscopy. The lifetime of a component of positron lifetime spectra determines the size of the voids and the intensity of the component determines the density of voids. From the results of irradiation damage in nickel, copper, aluminum, platinum, Cu-Ni alloy, Cu-B alloy, A1-Li alloy, iron, molybdenum and tantalum, it is concluded that gaseous impurity plays a quite important role for selecting whether bubbles and voids or collapsed vacancy loops are formed. This selection will be probably made at a fairly early stage, i.e., when several vacancies coagulate in a cluster.

The vacancy dislocation loop microstructure formed during heavy-particle bombardment

The magnitude of the steady-state vacancy loop dislocation density resulting from the partial collapse of collision cascades, and the irradiation dose necessary to attain this state, are estimated by means of rate theory. The effects of dislocations of other than vacancy-loop type, of voids, and of the simultaneous injection of self-ions (such as occurs in a simulation experiment) are incorporated within the model. Analytical approximations for the vacancy loop dislocation density and time to steady are presented for various limiting cases of dose rate and temperature. The implications of the results for the void growth rate are presented in a companion paper.

The sink strength of dislocation loops and their growth in irradiated materials

The sink strength of a circular dislocation loop is obtained for use in the rate theory model of microstructure evolution in irradiated materials. The dependence on loop size is obtained using the embedding procedure in the effective rate theory continuum. It is shown that the sink strength increases with increasing loop size. The result is applied to explain the observed growth of vacancy loops in certain irradiated materials.

Damage structure in zirconium alloys neutron irradiated at 573 to 923 k

The microstructures of annealed zirconium, zircaloy-2 and Zr-2.5 wt% Nb and of quenched-and-aged Zr-2.5 wt% Nb containing α' were studied after neutron irradiation to fluences of ≈1 × 10 25 n/m 2 , >0.1 MeV, in the temperature range 573 to 923 K. The principal form of damage was dislocation loops which increased in size and decreased in density with increasing temperature and which did not exist above 773 K. The loops lay primarily on prism planes and their Burgers' vector was consistent with 1 3a〈11 2 ̄ 0〉 . Half or more of the loops were of vacancy type. There was no dislocation network and no voids. A few gas bubbles were identified. An irradiation-enhanced precipitate of β-Nb formed from the α-phase in annealed Zr-2.5 wt% Nb. It is suggested that the absence of voids is related to the presence of vacancy loops and the lack of dislocation tangles, which indicate little or no net preferred absorption of self interstitials.

Influence of radiation-damage evolution on lattice-location measurements for Yb and Au in iron

The influence of radiation damage on the lattice location of heavy impurities (Yb and Au) implanted in iron is studied by channeling experiments. The nature of the impurity-radiation-damage interaction has been modified by annealing of room-temperature implanted samples or high-temperature implantation. The value of the corrected extinction ratio $\ensuremath{\epsilon}$ measured in several crystallographic directions on room-temperature implanted Yb and Au impurities cannot be interpreted uniquely in terms of different site populations. The annealing- and implantation-temperature dependences of the ratio $\ensuremath{\epsilon}$ for Yb-implanted Fe are very different. Upon annealing, the value of $\ensuremath{\epsilon}$ is unchanged up to 450\ifmmode^\circ\else\textdegree\fi{}C and then drops abruptly. In hot-implant experiments, the extinction ratio starts to fall at \ensuremath{\sim}150\ifmmode^\circ\else\textdegree\fi{}C when vacancies become mobile. Vacancy-assisted diffusion is suggested to cause the changes of $\ensuremath{\epsilon}$ in both experiments. The temperature dependence of $\ensuremath{\epsilon}$ for the (100) plane is found to differ from that in other directions. This planar effect suggests that Yb impurities move preferentially in the (100) plane, which is the plane of vacancy loops in Fe. A quantitative analysis of these lattice-location results and of related hyperfine-interaction results is presented in a companion paper.

The effect of damage rate on void growth in metals

The rate theory formulation of void growth was utilized to analyze the effects of damage rate on metal swelling. In particular, the swelling behavior of 316 SS was modeled as a function of temperature, over a range of displacement damage rates between 10 −6dpa/s and 10 −3dpa/s. Detailed analysis of the rate processes for point defect annihilation, migration, and loss to sinks indicated that small vacancy loops limit void growth at high damage rates. The reduction of void growth rates by vacancy emission from voids was found to be shifted towards higher temperature at higher displacement rates. In effect, the peak swelling temperature as well as the upper cutoff temperature for swelling are increased as the displacement rate is increased. The influence of constant or rate dependent nucleation conditions on the final swelling was investigated and it was shown that the initial microstructure before the growth stage essentially determines the peak swelling temperature. When appropriate empirical expressions for void and loop densities were used, the final peak swelling temperature shift agrees reasonably well with experimental data.

A stochastic theory for clustering of quenched-in vacancies—IV. Continuum model applied to the formation of stacking fault tetrahedra and vacancy loops

The continuum model for the growth of clusters developed in the previous paper (paper III) is applied to the formation of stacking fault tetrahedra in quenched gold and the formation of faulted vacancy loops in quenched aluminium. The results of the theory namely the distribution of the clusters as a function of their size and time, and the average size and the total density of the clusters as a function of time and the ageing temperature are shown to be in good agreement with the experimental results.

Stochastic theory for clustering of quenched-in vacancies—1. General mathematical properties

The problem of clustering of quenched-in vacancies into various types of extended defects is considered. A master equation for the evolution of the concentration of clusters of various sizes is written down with general transition rates. It is shown that this model represents a continuous time non-stationary Markoff process. A particular choice of transition rates corresponding to the formation of vacancy loops and stacking fault tetrahedra is considered in some detail. It is shown that this choice of transition rates allows us to obtain the solution for the concentration of the single vacancy units, and hence yields some information on the nucleation time. Further, the transition matrix becomes stationary and doubly stochastic due to the short time constant of the concentration of single vacancy units. This in turn leads to an unphysical stationary state. Finally we show how the rate equations for the irradiated situation can be written down and derive the phenomenological rate equations that are conventionally used.

Positron annihilation studies on electron- and α-particle-irradiated 75Nil3Crl2Fe alloys

Abstract Doppler broadening of the 511 keV annihilation radiation and electrical resistivity measurements have been performed during isochronal annealing of electron- and on α-particle-irradiated 75Nil3Crl2Fe alloys. The annealing behaviour of the positron annihilation parameters supports a simple two-stage recovery behaviour of the electron-irradiated alloy, for which the first stage below 200 K is attributed to the migration of interstitial atoms and the stage between 350 and 660 K to the migration of the radiation-induced vacancies. No formation of microvoids was observed. During both interstitial and vacancy migration a resistivity increase was observed. These increases are attributed to a redistribution of alloying atoms in the form of small precipitates. The a-particle-irradiated 75Nil3Crl2Fe alloy exhibited a small increase of the residual resistivity between 420 and ∼750 K. Both changes are probably due to continuous growth of defect clusters. Between ∼750 and 950 K both the resistivity and the lineshape parameter showed a pronounced decrease, indicating thermal dissolution of vacancy loops.

Characterization of neutron irradiation damage in zirconium alloys — an international “round-robin” experiment

The results are given of an international “round-robin” experiment to study the nature of the damage structure in neutron irradiated zirconium and zircaloy-2 using transmission electron microscopy. The damage structure consists entirely of 1 3 α<11 2 ̄ 0> dislocation loops and no evidence has been found for c-component loops. Both vacancy and interstitial loops were found in specimens irradiated at 400 °C, with an excess of vacancy loops. Quantitative measurements of loop size distributions and loop concentrations are reported. All specimens exhibited “corduroy” contrast to varying degrees. The importance of choice of imaging conditions to minimize the contrast from thin foil artefacts such as oxide films and surface hydrides is stressed. The significance of the results is briefly discussed with reference to current theories of irradiation growth.

The effect of vacancy loops on the swelling of irradiated materials

Calculations by Bullough, Eyre and Krishan [1] indicated that the vacancy loops produced in damage cascades might be important up to the peak swelling temperature during neutron irradiations. This represents a potential source of error for electron irradiation experiments, which do not produce damage cascades. More realistic calculations by the present authors, using revised electron swelling data for 316 stainless steel, can satisfactorily explain the observed neutron and nickel ion swelling behaviour of this steel if much smaller vacancy clusters are produced, in accord with Straalsund. The calculations show that the athermal production of vacancy loops does not affect neutron swelling above ≈ 450°C, so that electron simulations are valid at elevated temperatures. Ion simulations are more complicated because the effect of the vacancy loops is temperature shifted upwards by at least 150°C, and is in danger of overlapping the high temperature cut-off in some cases.

Numerical evaluation of combined self-ion injection and vacancy loop production in heavy-ion irradiations

Self-ion injection during heavy-ion bombardment of steels has been proposed as an additional mechanism to cascade damage for the reduction in void swelling compared to electron irradiation. Calculations on pure nickel have been made to demonstrate the efficiency of this mechanism in reducing the swelling, but in the absence of cascade (vacancy loops) effects. Recently a purely analytic evaluation by Brailsford has been used to treat the combined self-ion-cascade damage situation. Due to the complicated nature of the analysis only certain limiting cases were treated; even so, that work indicated that the competition between these mechanisms would lead to quite different results from those obtained without vacancy loops on pure nickel. Brailsford makes a plea for numerical calculations including both effects in order to establish the relative importance of each. The present work describes such a numerical study, with the void-swelling results for ST M316 steel chosen as the test vehicle. For the conditions prevailing we are able to establish the principal features of the swelling and show that the self-ion injection has only a small influence.

Heavy-ion irradiation of α-iron

Abstract In this paper we report the results from a transmission electron microscope study of α-iron after irradiation with heavy ions. No visible damage was observed following a low dose of self-ions in the energy range 40–240 keV. This is in contrast to the results from other pure metals where visible damage is produced after self-ion irradiation. Damage, in the form of small vacancy loops, was observed as the incident ion mass was increased, and quantitative results are presented on the dependence of both the defect yield and the defect size distribution on the ion mass. The Burgers vectors of the vacancy loops formed from 80 keV W+ ions are analysed and it is shown that both of the possible perfect loop Burgers vectors are present in the foils, i.e. a/2〈111〉 and a〈100〉. Finally, the sensitivity of the defect yield on ion mass and the nucleation of the a〈100〉 loops are discussed.

The irradiation-creep strain produced by vacancy loops

When metals are irradiated with neutrons or ions, vacancy loops are formed by the athermal collapse of displacement cascades. On the application of a uniaxial stress, those loops with normals aligned with the applied stress absorb irradiation-produced interstitials and thermally emit vacancies at a greater rate than the non-aligned loops. This mechanism ensures that the vacancy loop distribution will be non-isotropic, thereby producing a shape change. In this paper the magnitude of the creep strain produced by this mechanism is calculated: it is shown that the vacancy loop mechanism gives rise to transient irradiation-creep strains only and that the magnitude of the transient strain is small. The results of the present analysis are critically compared with previous work.

Vacancy injection during oxidation—A re-examination of the evidence

During oxidation of a pure metal the transfer of atoms from metal to oxide lattice may involve the generation of a counterflow of vacancies into the substrate. Such a process, known as vacancy injection, has received widespread attention in recent years. In this paper it is argued that much of the evidence quoted in support of injection is capable of alternative explanation. In particular, it is suggested that the growth of intergranular voids in metal substrates during oxidation is not due to vacancy injection from the interface but is a consequence of the induced tensile stress causing void growth by the Hull-Rimmer mechanism. It is also proposed that changes in the rate of vacancy loop growth in electron microscope foils upon changing the annealing atmosphere is due to alterations in the level of induced stress. If vacancies are not injected then they must be destroyed at the interface and this may seem difficult to reconcile with the fact that the interfaces of inert, non growing, oxides are not normally good sinks for metal vacancies. It appears that in order for vacancies to be created or destroyed at a two phase interface, atomic movements in each phase is required; it may be for this reason that the diffusional properties of an oxide-metal interface changes so radically when the oxidation process itself has ceased to occur.

α-Particle irradiation induced precipitation and phase instability in concentrated Fe-Cr-Ni alloys

Abstract Resistivity annealing of three different Fe-Ni-Cr alloys was investigated after α-particle irradiation at 320 K. In order to obtain a correlation between resistivity behaviour and microstructural changes, TEM studies were performed after specific annealing temperatures. The main resistivity changes can be explained in terms of radiation enhanced nucleation and growth of precipitates. After α-irradiaton and annealing black-white contrast images could be observed by TEM. Up to annealing temperatures of 800 K these images were attributed to vacancy loops and/or precipitates. The defect images which remain after annihilation at about 850 K. are attributed to precipitates with uniaxial strain in directions and with negative misfit volume.

Defect clusters in heavy-ion irradiated nickel and nickel alloys

Low-dose (≲1012ions/cm2) heavy-ion irradiation gives a convenient method of studying some aspects of fast-neutron radiation damage and has now been studied using transmission electron microscopy in a wide variety of metals and alloys (e.g. see the reviews by Eyre 1973 and Wilkens 1975). From these studies a consistent picture of the development of the damage structure has emerged. In most cases small vacancy loops are observed, produced heterogeneously at the sites of displacement cascades by the collapse of vacancy-rich ‘depleted zones’. The interstitial component of the damage is usually lost to the foil surfaces and is not observed. There have been surprisingly few investigations of heavy-ion damage in materials of technological importance. However, it has been noted that cascade collapse appears to take place less readily in complex alloys such as steels than in pure metals such as copper (e.g. Williams and Eyre 1976) but few attempts have been reported to explore this effect systematically.

A three-stage model for the development of secondary defects in ion-implanted silicon

Abstract A three-stage model to explain how the secondary defects consisting of interstitial dislocation loops evolve from the primary defects in ion-implanted silicon is presented. Crystals implanted to an ion dose below Dc (critical dose which forms a continuously damaged layer), such that the primary damage clusters do not overlap, were studied. The model suggests that the Frenkel pairs formed by ion impact produce submicroscopic clusters of vacancies and interstitials which are stable up to about 900 K. Upon heating to a higher temperature the smallest interstitial clusters emit mobile interstitials and/or the vacancy clusters emit mobile vacancies. The larger clusters grow and convert to dislocation loops. Vacancy loops shrink and disappear; interstitial loops grow because of the excess of interstitial'. The total area per unit area of interstitial loops remaining after a high temperature anneal above 1100 K corresponds to the number per unit area of the implanted atoms. The implication of this is that for vacuum and dry nitrogen anneals the surface is not important as a sink or source for point defects and that the annealing processes occur almost entirely within the buried damaged region.

In situstudy of radiation damage in thin foils of gold by high voltage electron microscopy

Abstract Thin foils of gold have been irradiated at room temperature using 2·5 MeV electrons in a high voltage electron microscope. By examination of defect clusters for several orientations and impurity contents (1 to 100 at. p.p.m.) it is possible to define four irradiation stages. During the first stage, interstitial dislocation loops grow with a t 1/3 time dependence only in thicker areas (< 1200 A). Stacking fault tetrahedra appear during stage 2 and exhibit ordering during stage 3; they collapse into vacancy loops during stage 4. During these latter stages, the time dependence for interstitial loops growth is no longer t 1/3. A kinetic model for defect concentrations has been developed, taking into account both surface diffusion and impurity concentration. Experimental and computed results both agree with regard to interstitial loop densities and sizes as a function of time, thickness and purity. The ordering processes of stacking fault tetrahedra are found to be consistent with models based on elas...

An X-ray topographic study of the behaviour of vacancy loops formed during the high-temperature oxidation of magnesium crystals

Abstract X-ray topography observations together with in situ weight-gain measurements have been used to study the defect structure of magnesium crystals oxidized at 550°C in air, as a function of oxide thickness. It is shown that during the initial stages of oxidation, i.e. where the oxide remains coherent, unfaulted loops, many with b = [0001], grow with increasing time of exposure. However, during the period of oxidation when decohesion of the metal-oxide interface becomes pronounced, the surface acts as a vacancy sink and continued annealing causes the loops to shrink and eventually disappear. The results are discussed in terms of previous electron microscopic observations reported on the oxidation characteristics of magnesium.